Bonus Assignment 1:
Based on the problem described below, formulate the problem as a linear program (you do not need to solve).
Completely describe your decision variables, objective, and constraints. You must use correct notation (i.e., if
you call a variable x1, then you should always call it x1). You may use summation notation. It is suggested that
you type this formulation for final submission. You may complete this work as a small group.
Maximum bonus points: 50
PROBLEM DESCRIPTION
NU Industries operates two manufacturing plants that produce three products: Widgets, Gadgets, and Flugels.
The finished products are shipped to the Distribution Center for final distribution to the customers. Five periods
of production are to be scheduled.
According to the Sales Department, the production requirements that must be met due to contracts during the
planning horizon are as follows:
Product Period 1 Period 2 Period 3 Period 4 Period 5
Widgets 70 125 185 190 200
Gadgets 200 300 295 245 240
Flugels 140 175 205 235 230
Also, the Marketing & Forecasting Department anticipates that NU Industries can cultivate additional demand
within the distribution area through effective advertising. The M&F Department projects that each $160
invested in advertising Widgets in a particular period creates additional demand for one Widget in the next
period. The corresponding values for Gadgets and Flugels are $120 and $180, respectively. However, the total
advertising budget is limited to $70,000 for the entire planning horizon.
Throughout the planning horizon, NU Industries will sell Widgets for $2490, Gadgets for $1990, and Flugels for
$2970. The products can be manufactured at either of NU’s Manufacturing Plants.
The Engineering Department has provided the following manufacturing and inventory data.
Plant A
The production requirements at Plant A are summarized below.
? Each Widget requires 194 pounds of Raw Material 1, 8.6 pounds of Raw Material 2, and 9.5 hours of Labor.
? Each Gadget requires 230 pounds of Raw Material 1 and 7.1 hours of Labor.
? Each Flugel requires 178 pounds of Raw Material 1, 11.6 pounds of Raw Material 2, and 11.1 hours of Labor.
Regular time labor availability is limited to 2500 hours in each period, but overtime can be scheduled in any
amount if necessary. Labor costs during periods 1 and 2 are $11/hour for regular time and $16.50/hour for
overtime. Labor costs are expected to rise by 5% at the end of period 2.
The product inventory area can store a combined maximum of 70 units, and inventory costs are as follows. It
costs $7.50 to store one Widget from one period to the next. The corresponding costs for Gadgets and Flugels
are $5.50 and $6.50, respectively.

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